Question

"Find the equation of line of best fit for the following values. Show your working"

Year : 1932 / 1936 / 1948 / 1952 / 1956 / 1960 / 1964 / 1968 / 1972 / 1976 / 1980
Height (cm) 197 / 203 / 198 / 204 / 212 / 216 / 218 / 224 / 223 / 225 / 236

Please help fast - this is very urgent!

Answer 1

The easiest way to do this problem is simply plug the lists into your calculator by pressing the stat button -> edit

Put year under L1 and height under L2

Then go to stat->calc->4:LinReg(ax+b)

this should bring up LinReg(ax+b) on your "home page"

press enter and you'll have your regression line otherwise known as the line of best fit.

Answer 2

Puzzhang: this is part of a problem and the whole problem is: "]Analytically create an equation to model the data in the above table." where the table is the data I just gave you. Does what you just said count as analytically solving this? If so, how could I write it down

Answer 3

to clarify: I just dropped down from HL math (International Baccalaurate) in the middle of the course of SL math where everyone else has done matrices. I only just started studying them now so I'm pretty noobish at matrices for now.

Answer 4

oops sorry there is a way to find the line of best fit manually but you have to know linear algebra.

Answer 5

hmm well another way of solving this under more advanced statistics ways.

Method:

slope can be derived from the equation slope=r*(Sy/Sx)
where r is the correlation coefficient, Sy is the standard deviation of the y variable, and Sx is the standard deviation of the x variable

the y intercept can be found by then using the equation
y intercept = (mean of the y data) - slope * (mean of x data)

Answer 6

the formula to find r, correlation coefficient is a pain in the retriceand I'd assume it'd be okay to find those values through the 1-var stats function on your calculator and have it spit out the standard deviations and r.

Feel free to reply if you have any more questions.

Answer 7

if you have data points between even x-axis intervals can you just add up the gradients of each line segment between each two two data points and divide by the number of line segments? I thought I could apply that to this

Answer 8

yeah i think that would work to find the slope. Then (mean of x values, mean of y values) is always a point on the best fit line. You'd get a point-slope regression that way :D

Answer 9

Yupp I think that's about it. I don't need to find the R^2 right here but there will be other things I need to find out after I'm finished with finding the line of best fit : P Thanks for now!